Spatio-temporal dynamics of the disordered Bose-Hubbard model

The transport properties of strongly interacting quantum systems are important characteristics and often defining of many-body phases. However, they are difficult to predict. We therefore have developed a novel measurement technique to study the near-equilibrium transport dynamics of a strongly interacting atomic lattice gas realizing the three-dimensional disordered Bose-Hubbard model. This quantitative measurement is, to our knowledge, the first of its kind in this type of experiment. We use this technique to measure the mobility μ of the gas across the transition from a superfluid to a disorder-induced insulator. This work is performed at finite temperature; at zero temperature, this is the superfluid to Bose glass transition. After preparing the gas, a small number of spatially localized atoms are transferred to a different hyperfine Zeeman state (or pseudo-spin state), a process we refer to as “spin tagging.” The two spin states can be imaged separately, enabling us to observe the spatial dynamics as the initially localized distribution relaxes towards equilibrium with the majority component. We model the dynamics using the Langevin equation, describing the evolution of a particle subject to both stochastic and deterministic forces. We use the solution to the Langevin equation for a stochastically-damped harmonic oscillator, which captures the effect of the harmonic potential trapping the atoms. In doing so, we treat the spin majority component as a background fluid the spin perturbation is moving through. The mobility characterizes the effect of the fluid on the spin-perturbed atoms. To confirm our interpretation of the measurement, we first investigate the relaxation of a weakly interacting thermal gas in a harmonic trap, where the underlying dynamics are well understood. In this regime the behavior is well explained by the rate of binary s-wave collisions. We vary the parameters of the gas and verify that the measured change in mobility is captured by the predicted change in collision rate. Having validated our understanding of the weakly interacting case, we next measure the dynamics of a strongly interacting disordered lattice gas. As disorder increases, relaxation is suppressed and the mobility decreases. The mobility is constant for the highest disorder strengths measured, indicative of the gas being in a maximally-localized state. This regime was the subject of a previous measurement from the DeMarco group, using a different probe of transport [1]. The two measurements are qualitatively consistent, further validating our technique.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Kowalski, Nicholas Edward

Contributors dc:contributor

• DeMarco, Brian
• Covey, Jacob
• Goldschmidt, Elizabeth
• Noronha, Jorge

• quantum simulation
• transport
• atomic physics
• quantum many-body
• Bose-Hubbard
• lattice gas

Statement dc:rights

• Copyright 2025 Nicholas Edward Kowalski

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/129162

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F129162